The continuous extension of the logarithmic double layer potential to the Ahlfors-regular boundary

TL;DR

This paper establishes a necessary and sufficient condition for the continuous extension of the logarithmic double layer potential to Ahlfors-regular boundaries, advancing understanding of boundary behavior in complex analysis.

Contribution

It provides a precise criterion for when the real part of the Cauchy-type integral extends continuously to Ahlfors-regular boundaries, a novel result in potential theory.

Findings

Identifies necessary and sufficient conditions for extension

Clarifies boundary behavior of logarithmic potentials

Enhances theoretical understanding of Ahlfors-regular boundaries

Abstract

For the real part of the Cauchy-type integral that is known to be the logarithmic potential of the double layer, a necessary and sufficient condition for the continuous extension to the Ahlfors-regular boundary is established.